6 ms·

Structure and Interpretation of Classical Mechanics (2014)

153 points by the-mitr 1y ago

noosphr 1y ago
I've often dreamed of a "Structure and interpretation" series of books. Scheme is pretty close to a universal computation substrate that provides enough ergonomics to be human understandable and writing anything out in it provides genuine illumination to what's going on under the hood. The "little" books are a tease of what that series could be.
- fouronnes3 1y ago
  I want to write Structure and Interpretation of Geometric Optics. I have an outline already in my notes and I'm convinced that the computing-first approach would benefit the field immensely. I've been learning optics for a while and writing a python library [0]. With a background in software it's very obvious that there is strong SICP vibes in lenses, refraction, etc. I just need someone to trust me and write me a check for 1 or 2 years salary so I can go full bunker mode and write it =) [0] https://victorpoughon.github.io/torchlensmaker/ https://victorpoughon.github.io/torchlensmaker/
  - noosphr 1y ago
    Sicp is not computation first. Sicp is understanding first. Doing the calculations automatically is a happy side effect of finding the right abstractions for describing what's happening physically and those abstractions being expressed in scheme already. E.g. Exercise 3.73 in SCIP asks how to implement an electrical circuit using a stream data structure. Because of all the work done beforehand you end up with an expression which describes the time behaviour of the circuit using the same expressions that describe its layout.
    - Iwan-Zotow 1y ago
      SICP
throwaway81523 1y ago
I didn't get anywhere trying to read this book. Then I watched a youtube video about calculus of variations and suddenly Lagrangian dynamics made total sense to me. I should probably try reading the book again.
- arunix 1y ago
  Do you remember which video that was?
  - griffzhowl 1y ago
    I don't know which it was but Dr. Jorge Diaz has an excellent video on Lagrangian mechanics as part of a series on quantum mechanics (this video just pertains to the formalism applicable classically) https://www.youtube.com/watch?v=QbnkIdw0HJQ https://www.youtube.com/watch?v=QbnkIdw0HJQ
  - throwaway81523 1y ago
    I don't remember the specific video but it was pretty elementary and got across the point that I had missed, you're not looking for a global optimum through some fancy operations on function spaces, you're just doing the old fashioned calculus thing of finding a maximum by setting a derivative to zero. Except you are doing that only at one endpoint of the mystery function, and its value (the boundary value) and derivative at that point (zero) are known, and you can work out the ODE that continues the solution. That's the Euler-Lagrange equation and suddenly everything makes sense.
Schiphol 1y ago
Does anybody know of a way to run the code in this book? I've tried a couple of times but never quite succeeded.
- nemoniac 1y ago
  You can run it in Racket with the SICP language. https://docs.racket-lang.org/sicp-manual/SICP_Language.html https://docs.racket-lang.org/sicp-manual/SICP_Language.html
  - Schiphol 1y ago
    Ah, nice, I'll try that. SICM in particular relies on numerical routines and things for scientific computing that this perhaps doesn't cover. We'll see. Thanks!
    - shawn_w 1y ago
      Someone ported the sicm/scmutils code to Racket: https://github.com/bdeket/rktsicm https://github.com/bdeket/rktsicm
      - soegaard 1y ago
        I think, this is the best way of running the SICM programs.
- noosphr 1y ago
  https://github.com/perceptual-ai/sicm-scheme-exercises https://github.com/perceptual-ai/sicm-scheme-exercises
  - Schiphol 1y ago
    This is what I tried, unsuccessfully if I remember correctly. I'll give it another try, thanks!
- gsf_emergency_4 1y ago
zkmon 1y ago
Funny that we call it classical. Newton wouldn't have called it so. Maybe we should categorize sciences based on the spatial scale at which they operate.A specific scale might define a world that has it's logic system, purpose, reasoning etc. For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality.
- kergonath 1y ago
  > Newton wouldn't have called it so. Of course. To him that would be modern mechanics. Or just mathematical natural philosophy, or whatever. > Maybe we should categorize sciences based on the spatial scale at which they operate. That would not be very useful, because there is no boundary. Nothing in general relativity says "below this everything is Newtonian". As a matter of fact we need to consider relativistic effects in quantum chemistry calculations that involve some heavy elements, at length scales smaller than 0.1 nm. Similarly, they just gave a Nobel prize for work on "Quantum properties on a human scale". > For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality. That is not at all how these frameworks are built, and that is not the dominant epistemological approach. The mainstream view is that there is a theory of everything that exists but is unknown to us, and that our various theories are approximations of that theory under different assumptions. They look categorically different because we don’t understand the overarching framework, not because nature is fundamentally different depending on scale. Also, I don’t see how the logic is fundamentally different between e.g. quantum mechanics and general relativity. Both rely heavily on things like Hamiltonian mechanics or symmetries. Some behaviours are different (like photons following geodesics and not straight lines, or superpositions of quantum states), but these are not a fundamental problem: a straight line is a limit case of a geodesic in a flat space, and a unique state is a limit case of superposition. I am not saying that everything is fine and we know everything, just that there is no clear boundary between the situations in which different theories are required and we cannot neatly decompose the universe into different realms where different theories apply.
  - zkmon 1y ago
    From my little knowledge, logic at Quantum scale appears quite different: * Things don't have their own location or identity * Spatial and temporal extents don't exist * Something may be true and false at the same time, or concept of true and false may not be defined * cause and effect goes for a toss, as behavior of time is different * Existence and non-existence co-exist, or come into existence together Similar effects at relatively-infinite scale (maybe purely mathematical) * Comparisons (big/small/equal) breakdown * Regular arithmetic and logic breaks down
michaelsbradley 1y ago
There’s also Functional Differential Geometry by the same Sussman and Wisdom: https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/9580/9580.pdf?dl=1 https://mitp-content-server.mit.edu/books/content/sectbyfn/b...
in_a_hole 1y ago
Does anyone know a text which justifies why the Lagrangian approach works? This text and many others I have encountered just start with the Principle of Least Action taken as given and go from there but I'm left wondering why we define the Action as this object and why we should expect it to be minimised for the physical trajectory in the first place. Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.
- wbpaelias 1y ago
  I believe Veritasium had a series where they derive the equivalence to Newton's laws
- ano-ther 1y ago
  It’s been a while but I seem to remember that the first book of Landau-Lifschitz‘ Theroretical Mechanics starts with a 20 page discussion that does this and culminates in the Lagrangian.
  - in_a_hole 1y ago
    I recently got hold of a copy of that. I started Hand & Finch - Analytical Mechanics but their woolly discussion of virtual work and virtual displacement was very frustrating and unenlightening. Perhaps I'll have a better time with L&L.
  - computerfriend 1y ago
    It's a great introduction to Lagrangian mechanics, but as I recall (it's also been a while for me), the motivation for extremising the action is also somewhat vaguely presented.
- nchagnet 1y ago
  Regarding the "why the action is this object" part of the question, I find that the easiest way to think about it is from the Hamiltonian perspective. There you can think of it as minimising energy along a trajectory. From that point, a Lagrangian is just a mathematical trick to express the symplectic structure differently. But if your question was more about "why minimizing something yields trajectories", I personally would argue this is beyond physics. As an empirical science, physicists have seen this kind of behaviour broadly (optics, classical mechanics, quantum mechanics) and just unified it as an overarching principle. Finally regarding the proof to newtonian mechanics, I don't have anything handy from the pure Newtonian perspective beyond the usual "minimises the lagrangian and your equations of motions look the same". However, you might be interested in proofs which show newtonian gravity as low energy approximation of general relativity. And since general relativity has a nice action formulation, it all gets nicely tied in. Hope this helps!
mindaslab 1y ago
What software they used to create this wonderful book?
dang 1y ago
Related. Others? Structure and Interpretation of Classical Mechanics (2015) - https://news.ycombinator.com/item?id=40805136 https://news.ycombinator.com/item?id=40805136 - June 2024 (12 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=31568387 https://news.ycombinator.com/item?id=31568387 - May 2022 (1 comment) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=23153778 https://news.ycombinator.com/item?id=23153778 - May 2020 (40 comments) Structure and Interpretation of Classical Mechanics (2015) - https://news.ycombinator.com/item?id=19765019 https://news.ycombinator.com/item?id=19765019 - April 2019 (87 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=9560567 https://news.ycombinator.com/item?id=9560567 - May 2015 (20 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=6947257 https://news.ycombinator.com/item?id=6947257 - Dec 2013 (37 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=1581696 https://news.ycombinator.com/item?id=1581696 - Aug 2010 (20 comments)
- Jtsummers 1y ago
  By the same authors so related but not SICM itself: Functional Differential Geometry (2012) [pdf] - https://news.ycombinator.com/item?id=7884551 https://news.ycombinator.com/item?id=7884551 - June 2014 (38 comments)

153 points by the-mitr 1y ago

I've often dreamed of a "Structure and interpretation" series of books. Scheme is pretty close to a universal computation substrate that provides enough ergonomics to be human understandable and writing anything out in it provides genuine illumination to what's going on under the hood. The "little" books are a tease of what that series could be.

fouronnes3 1y ago
I want to write Structure and Interpretation of Geometric Optics. I have an outline already in my notes and I'm convinced that the computing-first approach would benefit the field immensely. I've been learning optics for a while and writing a python library [0]. With a background in software it's very obvious that there is strong SICP vibes in lenses, refraction, etc. I just need someone to trust me and write me a check for 1 or 2 years salary so I can go full bunker mode and write it =) [0] https://victorpoughon.github.io/torchlensmaker/ https://victorpoughon.github.io/torchlensmaker/
- noosphr 1y ago
  Sicp is not computation first. Sicp is understanding first. Doing the calculations automatically is a happy side effect of finding the right abstractions for describing what's happening physically and those abstractions being expressed in scheme already. E.g. Exercise 3.73 in SCIP asks how to implement an electrical circuit using a stream data structure. Because of all the work done beforehand you end up with an expression which describes the time behaviour of the circuit using the same expressions that describe its layout.
  - Iwan-Zotow 1y ago
    SICP

throwaway81523 1y ago

I didn't get anywhere trying to read this book. Then I watched a youtube video about calculus of variations and suddenly Lagrangian dynamics made total sense to me. I should probably try reading the book again.

arunix 1y ago
Do you remember which video that was?
- griffzhowl 1y ago
  I don't know which it was but Dr. Jorge Diaz has an excellent video on Lagrangian mechanics as part of a series on quantum mechanics (this video just pertains to the formalism applicable classically) https://www.youtube.com/watch?v=QbnkIdw0HJQ https://www.youtube.com/watch?v=QbnkIdw0HJQ
- throwaway81523 1y ago
  I don't remember the specific video but it was pretty elementary and got across the point that I had missed, you're not looking for a global optimum through some fancy operations on function spaces, you're just doing the old fashioned calculus thing of finding a maximum by setting a derivative to zero. Except you are doing that only at one endpoint of the mystery function, and its value (the boundary value) and derivative at that point (zero) are known, and you can work out the ODE that continues the solution. That's the Euler-Lagrange equation and suddenly everything makes sense.

Schiphol 1y ago

Does anybody know of a way to run the code in this book? I've tried a couple of times but never quite succeeded.

nemoniac 1y ago
You can run it in Racket with the SICP language. https://docs.racket-lang.org/sicp-manual/SICP_Language.html https://docs.racket-lang.org/sicp-manual/SICP_Language.html
- Schiphol 1y ago
  Ah, nice, I'll try that. SICM in particular relies on numerical routines and things for scientific computing that this perhaps doesn't cover. We'll see. Thanks!
  - shawn_w 1y ago
    Someone ported the sicm/scmutils code to Racket: https://github.com/bdeket/rktsicm https://github.com/bdeket/rktsicm
    - soegaard 1y ago
      I think, this is the best way of running the SICM programs.
noosphr 1y ago
https://github.com/perceptual-ai/sicm-scheme-exercises https://github.com/perceptual-ai/sicm-scheme-exercises
- Schiphol 1y ago
  This is what I tried, unsuccessfully if I remember correctly. I'll give it another try, thanks!
gsf_emergency_4 1y ago

zkmon 1y ago

Funny that we call it classical. Newton wouldn't have called it so. Maybe we should categorize sciences based on the spatial scale at which they operate.A specific scale might define a world that has it's logic system, purpose, reasoning etc. For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality.

kergonath 1y ago
> Newton wouldn't have called it so. Of course. To him that would be modern mechanics. Or just mathematical natural philosophy, or whatever. > Maybe we should categorize sciences based on the spatial scale at which they operate. That would not be very useful, because there is no boundary. Nothing in general relativity says "below this everything is Newtonian". As a matter of fact we need to consider relativistic effects in quantum chemistry calculations that involve some heavy elements, at length scales smaller than 0.1 nm. Similarly, they just gave a Nobel prize for work on "Quantum properties on a human scale". > For example, quantum scale, human scale and cosmic scales have their own physics, logic and causality. That is not at all how these frameworks are built, and that is not the dominant epistemological approach. The mainstream view is that there is a theory of everything that exists but is unknown to us, and that our various theories are approximations of that theory under different assumptions. They look categorically different because we don’t understand the overarching framework, not because nature is fundamentally different depending on scale. Also, I don’t see how the logic is fundamentally different between e.g. quantum mechanics and general relativity. Both rely heavily on things like Hamiltonian mechanics or symmetries. Some behaviours are different (like photons following geodesics and not straight lines, or superpositions of quantum states), but these are not a fundamental problem: a straight line is a limit case of a geodesic in a flat space, and a unique state is a limit case of superposition. I am not saying that everything is fine and we know everything, just that there is no clear boundary between the situations in which different theories are required and we cannot neatly decompose the universe into different realms where different theories apply.
- zkmon 1y ago
  From my little knowledge, logic at Quantum scale appears quite different: * Things don't have their own location or identity * Spatial and temporal extents don't exist * Something may be true and false at the same time, or concept of true and false may not be defined * cause and effect goes for a toss, as behavior of time is different * Existence and non-existence co-exist, or come into existence together Similar effects at relatively-infinite scale (maybe purely mathematical) * Comparisons (big/small/equal) breakdown * Regular arithmetic and logic breaks down

michaelsbradley 1y ago

There’s also Functional Differential Geometry by the same Sussman and Wisdom: https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/9580/9580.pdf?dl=1 https://mitp-content-server.mit.edu/books/content/sectbyfn/b...

in_a_hole 1y ago

Does anyone know a text which justifies why the Lagrangian approach works? This text and many others I have encountered just start with the Principle of Least Action taken as given and go from there but I'm left wondering why we define the Action as this object and why we should expect it to be minimised for the physical trajectory in the first place. Failing a full derivation from the ground up, a proof of the equivalence to Newtonian mechanics would be interesting.

wbpaelias 1y ago
I believe Veritasium had a series where they derive the equivalence to Newton's laws
ano-ther 1y ago
It’s been a while but I seem to remember that the first book of Landau-Lifschitz‘ Theroretical Mechanics starts with a 20 page discussion that does this and culminates in the Lagrangian.
- in_a_hole 1y ago
  I recently got hold of a copy of that. I started Hand & Finch - Analytical Mechanics but their woolly discussion of virtual work and virtual displacement was very frustrating and unenlightening. Perhaps I'll have a better time with L&L.
- computerfriend 1y ago
  It's a great introduction to Lagrangian mechanics, but as I recall (it's also been a while for me), the motivation for extremising the action is also somewhat vaguely presented.
nchagnet 1y ago
Regarding the "why the action is this object" part of the question, I find that the easiest way to think about it is from the Hamiltonian perspective. There you can think of it as minimising energy along a trajectory. From that point, a Lagrangian is just a mathematical trick to express the symplectic structure differently. But if your question was more about "why minimizing something yields trajectories", I personally would argue this is beyond physics. As an empirical science, physicists have seen this kind of behaviour broadly (optics, classical mechanics, quantum mechanics) and just unified it as an overarching principle. Finally regarding the proof to newtonian mechanics, I don't have anything handy from the pure Newtonian perspective beyond the usual "minimises the lagrangian and your equations of motions look the same". However, you might be interested in proofs which show newtonian gravity as low energy approximation of general relativity. And since general relativity has a nice action formulation, it all gets nicely tied in. Hope this helps!

mindaslab 1y ago

What software they used to create this wonderful book?

dang 1y ago

Related. Others? Structure and Interpretation of Classical Mechanics (2015) - https://news.ycombinator.com/item?id=40805136 https://news.ycombinator.com/item?id=40805136 - June 2024 (12 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=31568387 https://news.ycombinator.com/item?id=31568387 - May 2022 (1 comment) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=23153778 https://news.ycombinator.com/item?id=23153778 - May 2020 (40 comments) Structure and Interpretation of Classical Mechanics (2015) - https://news.ycombinator.com/item?id=19765019 https://news.ycombinator.com/item?id=19765019 - April 2019 (87 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=9560567 https://news.ycombinator.com/item?id=9560567 - May 2015 (20 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=6947257 https://news.ycombinator.com/item?id=6947257 - Dec 2013 (37 comments) Structure and Interpretation of Classical Mechanics - https://news.ycombinator.com/item?id=1581696 https://news.ycombinator.com/item?id=1581696 - Aug 2010 (20 comments)

Jtsummers 1y ago
By the same authors so related but not SICM itself: Functional Differential Geometry (2012) [pdf] - https://news.ycombinator.com/item?id=7884551 https://news.ycombinator.com/item?id=7884551 - June 2014 (38 comments)